I haven't looked at your unformatted code closely, but I spotted a "NullPointerException" message at top of your stacktrace. This simply means that some object reference at the mentioned line, inside the mentioned method of the mentioned class is null while your code is trying to access/invoke it.
If my blurry little eyes don't (again) deceive me, you're trying to invoke a method on an object that doesn't exist. Hint: there's a "Code" button on the message editor. Use it to generate tags that will display your code better.
JSF will construct JavaBeans for you, but only if you define them as managed beans in the faces-config file. Apparently you did not do that for userManagedBean .
Good practice in JEE would be that the backing bean would be a managed bean and it would talk to a DAO/service object which would handle the persistence-related functions. The JEE framework would inject the persistence manager (EntityManager).
As far as it goes, I've got a VERY long list of why webapps should generally NOT have their own login code, but instead use the security system that Sun created for J2EE wherever possible.
An IDE is no substitute for an Intelligent Developer.